characterization and modeling of schot- tky diodes … · schottky diode is vast; a widely used...

Progress In Electromagnetics Research, Vol. 131, 457–475, 2012

CHARACTERIZATION AND MODELING OF SCHOT-TKY DIODES UP TO 110GHz FOR USE IN BOTH FLIP-CHIP AND WIRE-BONDED ASSEMBLED ENVIRON-MENTS

K. Zeljami1, J. Gutierrez1, J. P. Pascual1, T. Fernandez1, *,A. Tazon1, and M. Boussouis2

1Department of Communications Engineering, University of Cantabria,Edificio I+D+I de Ingenierıa de Telecomunicaciones, Plaza de la Cien-cia, S/n Santander 39005, Spain2Physics Department, Faculty of Sciences, University of AbdelmalekEssaadi, Tetouan, Morocco

Abstract—This paper presents a wideband model, from DirectCurrent (DC) to W band, for a single Anode Schottky Diode basedon a commercial VDI chip. Different measurements have beenperformed to obtain a complete large-signal equivalent circuit modelsuitable for the device under consideration up to 110 GHz, and forits integration in planar circuits. The modeling has been done usinga combination of DC measurements, capacitance measurements, andRF scattering measurements. The test structure for on-wafer S-parameter characterization has been developed to obtain an equivalentcircuit for Coplanar to Microstrip (CPW-Microstrip) transitions, thenverified with 3D Electromagnetic (EM) tools and finally used to de-embed device measurements from empirical data results in W band.3D EM simulation of the diodes was used to initialize the parasiticparameters. Those significant extrinsic elements were combined withthe intrinsic elements. The results show that the proposed method issuitable to determine parameters of the diode model with an excellentfit with measurements. Using this model, the simulated performancefor a number of diode structures has given accurate predictions upto 110 GHz. Some anomalous phenomena such as parasitic resistancedependence on frequency have been found.

Received 13 July 2012, Accepted 31 August 2012, Scheduled 17 September 2012* Corresponding author: Tomas Fernandez ([email protected]).

458 Zeljami et al.

1. INTRODUCTION

The concept of Terahertz Electronics has emerged during the lasttwo decades and draws increasing attention in security applicationssuch as imaging systems [1, 2], security screening systems, geneticengineering, pharmaceutical quality control and medical imaging. Inthese frequency bands simplicity of non linear devices is required tominimize parasitic effects. Different types of diodes, such as avalanchediodes [3] or Schottky diodes, could be a natural choice.

Particularly Schottky diodes have been widely accepted as a usefulsolution for Terahertz (THz) applications. These components areused for design of mixers and frequency multipliers in sub-millimeterwavelengths [4]. In addition, the planar diode opens up the possibilityof diode circuit integration [5].

The advantages of GaAs Schottky diodes include monopolaroperation, high mobility and low noise figures at room temperature.They are presently considered as mature devices, but they are still thesubject of investigation concerning their optimization. For operationin millimeter and sub-millimeter wavelength, and for high-frequencyapplications, n-doped GaAs is the typical semiconductor used in themetal- semiconductor system but the performance of a GaAs Schottkydiode is still limited by its parasitic elements [6] and the losses due toskin effects [7]. Moreover, the geometrical design of Schottky diodesis a very critical factor in determining the device performance. Thus,systematic studies of the Schottky diode’s parasitic elements and high-frequency losses are very crucial in achieving the design goals.

Generally in RF design, a diode can be modeled as a combinationof resistance and capacitance, both bias-dependent. The Schottkydiode model consists of both, linear and nonlinear parts. The nonlinearpart corresponds to the metal-semiconductor junction, and the linearpart contains everything else [4]. The construction of millimeterand sub-millimeter-wave Schottky diode-based circuits relies on validcomponent models in the design stage. Therefore, no parasitic effectsintroduced by the diode package elements can be neglected at thisfrequency, and accurate modeling of them is necessary. Several studieson diode modeling have been performed [8, 9].

In this paper, we describe the characterization of a high-performance Schottky diode for millimeter wavelengths. Modelextraction is based on different measurements and computer-aidedparameter extraction. The different measurements were: directcurrent (DC) characteristics, capacitance measurements, scattering(S) parameter measurements and measurements of the assembly ofCoplanar to Microstrip bonded transitions used to achieve the complete

Progress In Electromagnetics Research, Vol. 131, 2012 459

final diode model up to 110 GHz. In accordance with the availabilityof measurement equipment, the measurements were carried out in twofrequency ranges: DC-50 GHz and 75–110 GHz.

2. DIRECT CURRENT (DC) CHARACTERIZATION OFSCHOTTKY DIODES

The intrinsic Schottky diode is modeled as a circuit containing fourphysical parameters [10]: a series resistance Rs, a shunt resistance Rj ,a Schottky diode reverse saturation current Is and a Schottky diodeideality factor η.

The dominant current transport mechanisms in state-of-the-artGaAs Schottky mixer diodes are the emission of electrons over thebarrier and the quantum mechanical tunneling of electrons throughthe barrier. A widely recognized model which takes into account bothof these effects is the thermionic-field emission model [11] generalizedI-V characteristics, Equation (1):

I(Vd) = Is

[exp

(q (Vd − IdRS)

ηkT

)− 1

]≈ Is exp

(q (Vd − IdRs)

ηkT

)(1)

where Is is the saturation current, Vd is the voltage across the Schottkybarrier, η is the ideality factor and Rs is the series resistance of thediode.

2.1. Extraction of the Resistance, Saturation Current andIdeality Factor

Direct Current (DC) measurements are the most common character-ization and testing method for Schottky diodes. This method firstperforms current-voltage measurements and then facilitates the char-acterization of the nonlinear properties of the Schottky diode when itis driven into the forward-biased state. In this part, we will performmeasurements that will lead us to obtain the parameters characteriz-ing the Schottky junction, which determine the conduction propertiesof these diodes when the forward bias is applied, and to obtain theparasitic resistance values Rs of the Schottky diode by fitting from thecurrent-voltage measurements [12].

Based on the Schottky diode Equation (1), a voltage-controlledcurrent source is used. The values of the current Id are injected andthe equivalent diode voltage V is measured. The voltage across theSchottky barrier is equal to an applied voltage minus any voltage dropacross the series resistance Rs that is, Vd = V − I ·Rs and at low levelsof polarization when the voltage drop across the series resistance Rs is

460 Zeljami et al.

negligible compared to the voltage drop in the space charge region [13],so Vd = V ;

Vd = IdRs +ηkT

qln

[Id/Is

](2)

Vd = V = 1/αLn(Id/Is

)(3)

Device parameters such as reverse saturation current (Is) and idealityfactor η can be found on the semilog-scale of the forward characteristicof the diode. They are found to be close to the nominal values providedin the device’s datasheet [14]. Typical forward curve Direct Current(DC) Measurements and the data fitted I-V curve are shown as a solidline in Figure 1.

The available literature describing resistance extraction of theSchottky diode is vast; a widely used approach focuses on the DCmeasurements. Measured I-V characteristics in a range of low voltageare least-square fitted to Equation (3). The result is considered the“ideal” I-V curve without the effect of the series resistance (Figure 2).Regarding the ideal part, the I-V relation maintains a constant slope ona semilog plot, as indicated by the straight line, at higher current levels,however, the voltage drop across the parasitic resistance becomessignificant with respect to the diode voltage drop, and the curvedeviates from this line.

The variation from the ideal diode performance is easily observedin the Figure 2. This deviation provides the necessary information toallow extraction of the parasitic resistance value. Figure 3 shows the

Voltage (V)

Curr

ent

(A)

Figure 1. Measured and model I-V characteristic results for the SingleAnode Schottky Diode.


Voltage (V)

Cur

rent

[m

A]

Figure 2. Extraction of the series resistances (forward I-V curve ofdiode plotted with current on logarithmic scale).

Vd (V)

Rd

(Ω)

Figure 3. Extraction of the series resistance of Single Anode diode(SA-Diode) from measurement voltage.

extraction of the series resistance from voltage measurements. At largevoltage values, the resistance increases slightly with increasing voltage,but it remains within the limit values given by the datasheet [14].

2.2. Capacitance Extraction

The capacitance of Schottky diodes is the key factor for the high-frequency performance of mixers, detectors or frequency multipliers.

462 Zeljami et al.

The usual form for the diode capacitance-voltage relationship, takinginto account the dependent junction capacitance, has been givenby [15, 16]:

Cj(V ) =dQ

dV=

Cj0(1− Vj

φbi

)γ (4)

where Cj0 is the zero-bias junction capacitance, Φbi is the built-inpotential, Vj is the junction voltage (Vj > 0) and the exponent γ isa function of the doping profile. The total capacitance of a Schottkydiode can be divided mainly into the junction capacitance and theparasitic capacitance. Using Equation (1), the total capacitance canbe expressed as:

Ctotal = Cj + Cpp = Cj(V ) =Cj0√(

1− Vd

φbi

) + Cpp (5)

Several methods have been proposed to determine the junctionand parasitic capacitances and built-in voltage [17, 18] of a Schottkydiode; in this work apparent capacitance of the diode chips wasmeasured in two ways: from on-wafer S-parameter measurementsand with low-frequency measurements using a LCR (Inductance-Capacitance-Resistance) meter. Differences between the two methodsare compared. The junction capacitance, along with some othercapacitance-voltage C-V parameters, is then obtained by fittingthe measurement results to a nonlinear capacitance expression(Equation (5)) in a least squares sense.

At lower microwave frequencies, when the diode is not yetconducting, the equivalent circuit of the diode can be reduced to a“π” network of capacitances [18], formed by the total capacitance CT

and small parasitic capacitances to the ground. CT is the sum ofthe junction capacitance Cj0 and the parasitic capacitances Cpp. Anaccurate estimation for the total capacitance can be extracted by fittingthe measured value of the transmission coefficient (Figure 4), which isdependent mainly on the total capacitance CT , the ratio between Cj0

and Cpp. The S parameters were measured from 2 GHz up to 50 GHz,however, for the capacitance extraction only, the frequency range 3–10GHz is used, according to the condition for the reduction of theequivalent circuit of the diode to only three capacitances.

The low-frequency measurements have been done using an AgilentE4980A LCR meter. Frequency is set at 1MHz. Measurements aredone on a Single Anode Diode flip-chip mounted on a test structure(Figure 5). The calibration was done by measuring an empty gap


with the same dimensions as the test structure with the diode; thisrepresents the parasitic capacitance correction for the measurement.Results are illustrated in Figure 6.

Comparing the capacitance curve results shown in Figure 7 forthe two capacitance determination techniques based on S-parametermeasurements and on LCR meter measurements [19], it can be seenthat the extracted values for the parasitic capacitance from theLCR meter are greater than those obtained using the S-parametertechnique. This may be due to the contact of the diode with the testfixture microstrip lines, which can cause the appearance of a largeparasitic capacitance and affect the correct measurements of all theextracted capacitance parameters of the diode.

freq, GHz

S

(dB

)21

Figure 4. Measurement of transmission coefficient and calculatedtransmission coefficient for the Single Anode Schottky Diode.

Figure 5. Simple test structure, flip-chip mounted discrete diode.

464 Zeljami et al.

Voltage (V)

Cap

acit

ance

to

tal

(fF

)

Figure 6. C-V Extraction. Equation (5) is fitted to total capacitancevalues measured with LCR meter.

Vd (V)

CT

(fF

)

-3 -2.5 -2 -1.5 -1 -0.5 0

60

55

50

45

40

35

30

25

20

15

10

Extraction from S parameter

Extraction from LCR meter

Figure 7. Measured and extracted total capacitances and othervoltage capacitance parameters, Equation (5) is fitted againstmeasured total capacitance values.

3. CHARACTERIZATION OF DIODES: SIMULATION(MODELING TOOLS)

The final goal of the characterization process is to develop a large-signalequivalent circuit of the device. This involves the characterization ofboth, intrinsic elements and parasitic elements of the device. This partdeals with the investigation of the parasitic elements introduced bycontacting pad air bridges, bond wires, and semiconductor substrate.


In this modeling work, suitable design and optimization methods havebeen implemented on two simulators: a 3D electromagnetic simulatorHFSS (Ansoft High Frequency Simulation Software) and a circuitsimulator ADS (Agilent Advanced Design System).

Once the significant extrinsic elements have been identifiedfrom the diode layer, their values can be determined using two-port measurements. As a starting point, amplitude and phasemeasurements of the anode reflection coefficient, S11, and the anodeto cathode transmission coefficient, S21, were taken at zero bias. Withrealistic initial estimates for the elements values based on the physicalstructure of the device using SEM (Scanning Electron Microscope)image (Figure 8), along with measurements taken from Direct CurrentDC up to high microwave frequencies; equal weighting was applied toall responses, across the whole frequency range.

A good optimization algorithm produces values that quicklyconverge to the correct values. When zero bias convergence has takenplace, the voltage dependency of Cj(v) and Rj(v) can be implementedusing a SDD (Symbolically-Defined-Device) module from ADS. Theerror function produced by the optimization algorithm should remainrelatively constant for all the potential bias points. Figure 8 showsa Single Anode Diode under consideration. The nominal overall chipdimensions of the diode are 600µm×250µm×100µm (length × width× thickness). It is connected with coplanar-to-microstrip transitions(model PROBE POINT TM1003 JmicroTM transition) [20]. Thisconfiguration is desirable to enable on-wafer measurements using aircoplanar probes, but in this case requires the use of wire bondingconnections. This chip connection procedure features low cost, highreliability, and high manufacturability [21].

Bonding Wires

Anode

padCathode

Diode Coplanar to

Microstrip Transitions

(a) (b)20 mµ Electron Image 1

Figure 8. (a) Single Anode Diode (SA-Diode) bonded with goldwires (diameter of 17µm and length 200µm–210µm at both sides).(b) Scanning Electron Microscope (SEM) image of a Single AnodeDiode.

466 Zeljami et al.

3.1. Equivalent Circuit Model of the Diode (LumpedElements: Intrinsic and Extrinsic)

The equivalent circuit model depends on the type of the diode, andon the surrounding circuitry. Figure 9 shows the equivalent circuitproposed for the discrete planar Schottky diodes under considerationin order to illustrate its integration in a microstrip circuit environmentincluding bonding wires. As with the previous low-frequency models,the distributed resistance and capacitance of the active layer aretransformed into a first order equivalent network represented by Rs

and Cj(v). The model accommodates forward bias with the junctionleakage resistance, Rj(v). This resistance is effectively an open circuitwith reverse bias [22].

The circuit includes a finger inductor Lp (estimated using theplanar inductor approximation [23]) and a pad-to-pad capacitor Cpp,which represents the capacitance between the two bonding pads ofthe diode. In parallel with the Schottky junction is the finger-to-padcapacitance component Cp, which represents the capacitance betweenthe anode contact finger and the underlying active GaAs. A set ofsimple lumped elements models parts inside and outside the diode:an ideal inductance L2 in series with resistor R represents the wireinductance and losses due to the metallization and wire bonding, aswell as radiation losses at the wire bends [24, 25]. The two shuntcapacitances close to the input and output ports (C1, C2) represent thesubstrate capacitance between the microstrip lines onto which the wireis bonded. Therefore, they are used to model the discontinuity betweenthe contact lines. The discontinuities on both sides are not necessarilyidentical since the planar diode structure is not completely symmetricand the length of the bond wires is not exactly the same on both sides.The inductor L1 represents end inductance caused by the wire bonds.Finally, the intrinsic device is represented through its characteristic

Figure 9. Single Anode lumped equivalent circuit for Schottky diodewith the extrinsic elements detailed.


elements: Rj is the nonlinear Schottky junction resistance that acts inparallel with the diode junction capacitance Cj , and the ohmic contactresistance is denoted by Rs. The equivalent values for each intrinsicelement component are extracted from measured Direct Current (DC)characteristics and scattering parameters with fixed RF power levels(≤ −30 dBm), and the diode unbiased and also reverse biased.

3.2. Characterization of Coplanar to Microstrip(CPW-Microstrip) Transitions

Coplanar to Microstrip transitions have been used to measurethe diode. The effect of the transitions can be removed fromthe measurements by applying the calibration proposed by themanufacturer. However, this calibration kit is not intended forthe 75–110 GHz band. In this case a generic calibration procedureplacing the measurement reference planes at the probe tips is used.Therefore, neither CPW-Microstrip transitions nor wire bonds can beautomatically de-embedded and the task of de-embedding parasiticeffects of these CPW-Microstrip transitions becomes a new concern.In this sense an electromagnetic model for two CPW-Microstriptransitions connected with a bond wire was developed for this work.This model will be used to de-embed device measurements fromempirical data results, which means isolating the performance of thediode by extracting the effect of the transitions from the measurements.

The CPW-Microstrip transitions are attached to a gold platedbrass as ground plane using a conductive epoxy and wire bonded to themicrostrip part. In this case a calibration using the generic procedurehas been performed (Cascade Probe LRM), by placing the measuringplanes in the positions (a) and (b) marked in Figure 10. Subsequently,the position of the reference plane may be changed in order to take into

Figure 10. The assembly of the two “Coplanar to Microstrip”transitions, connecting with the bond wire.

468 Zeljami et al.

account the effects of the two CPW-Microstrip transitions and bondwire. To calibrate the system in the plane of coplanar probes, LRRMcalibration (LINE, REFLECT, REFLECT, MATCH) [26], as well ascoplanar standards (Cascade Microtech ISS 101-190), have been used.The S-parameter measurement of the test sample has been performedusing a network analyzer in the 2–50 GHz range and a PNA-X withmillimeter-wave head extensions in the W-band.

To validate the response obtained in the measurements carriedout, the 3D electromagnetic simulator HFSS (High FrequencyStructure Simulator) has been used. In this way, the assembly of theCPW-Microstrip transitions has been performed as is shown in theFigure 11, in order to obtain the behavior of the scattering parametersas a function of frequency as shown in the plots Figure 12. Thesimulations have been executed from 1 up to 110GHz. Close fitting isobtained between simulation and measurement.

Figure 11. 3D view of the assembly of the two transitions, connectedwith the bond wire.

freq, GHz freq, GHz

S

(dB

)21

S

(dB

)11

Figure 12. Simulation of the assembly of the two transitions,connected with the bond wire.


3.3. Measurement Setup

Before the measurements were made, the system was calibrated atthe probe tips using a Cascade probe LRRM (LINE, REFLECT,REFLECT, MATCH) calibration kit. In this way, the measurementsare carried out in two different frequency ranges: (1–50GHz) andin W-band (75–110 GHz), at an ambient temperature of 293K atseveral bias voltage points from −3.5 to 0V. The operation of themeasurement set-up has been checked in the first place by measuringin the frequency band 1–50 GHz, using TRL calibration (THROUGH,REFLECT, LINE) to correct the effect of the transitions and to obtainthe scattering parameters of the diode with the bond wire in the inputand output of the device. A value of −30 dBm of input power hasbeen established to carry out the measurements and reverse biasinghas been applied to the diode.

In the frequency band 75–110 GHz, the measurement equipmentconsists of a microwave network analyzer, N5242A PNA-X, whichcan only obtain S-parameters up to 26.5GHz. For this reason twoexternal millimeter-wave (VNA-extensions) [27] heads were connectedto PNA-X for measuring S-parameters in W band. A waveguide tocoaxial transition (model 35WR10WF) and 1 mm-coaxial cables, whichallow us to measure over the entire W band (75–110GHz) and finally,coplanar probes (Model 110H) with a spacing (“pitch”) of 125µmare necessary to measure on-wafer. These measuring tips serve asadapters between the wires and measuring contact surfaces (“Pads”)of the structure.

Direct measurements placing a couple of probe tips on the anodeand cathode pads were done to verify that coherence of the model isnot affected by the surrounding parasitic effects associated with wirebonding and transitions. A special 150µm pitch differential probe withtwo contacts (Signal-Ground) was placed just on the pad-to-pad diodegap, as can be seen in Figure 13.

S G

Figure 13. Single Anode Diode, measurement with probe (50A-GS-150-P).

470 Zeljami et al.

Figure 14. Reflection coefficient simulated and measured for SchottkyDiode with probe (50A-GS-150-P).

Results have been verified by comparing the reflection parameter,S11 (Figure 14), through low frequency diode measurements (up to20GHz) with the equivalent circuit model modified for this verificationremoving the components which represent the test fixture (bonding,Transitions, etc.) and taking into account only grounding capacitanceVery good agreement between the measurement and the model wasachieved.

3.4. ResultsS-parameter measurements and simulation results at 1–110 GHz for aCoplanar to Microstrip transitions de-embedded Single Anode diode,using the equivalent circuit model shown in Figure 9, are represented inFigure 15, Figure 16. It can be seen from the figures that the equivalentcircuit model describes the behavior of the diode well. The reflectionand transmission coefficients from the equivalent circuit simulation arerepresented, first for the unbiased diode (0 V) (Figure 15) and thenfor the reverse-biased diode (−3V) (Figure 16). De-embedding ofCoplanar to Microstrip transitions in W band was done using ADS.

It should be noted here that our model takes into accountthe increase of the wire bonding series resistance caused by theskin effect [25] at frequencies above 50GHz and eventually by someother measurement uncertainties. The study of the extent of thiseffect becomes difficult at this frequency band, as measurementsare limited by calibration accuracy and some possible inaccuracyin the determination of other equivalent circuit parameters such asfinger inductance, parasitic capacitances, etc.. Nevertheless, theincrease in resistance in W band was consistently found when fittingmeasurements of several devices. The resulting extracted modelparameters are listed in Table 1.


-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Figure 15. S-parameter simulation and measurement for SchottkyDiode using circuit in Figure 9. Diode is unbiased (0 V).

S (2

,2)

472 Zeljami et al.

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Figure 16. S-parameter simulation and measurement for SchottkyDiode using circuit in Figure 8. Diode was biased (−3V).

Table 1. Extracted parameters of the Schottky diode underconsideration.

Parameters Symbol Value

Saturation current (A) Isat 9.97593 · 10−13

Ideality factor η 1.28

nkT/q (1/V) α 30.31

Zero junction capacitance (fF) Cj0 24

Series resistance (Ω) Rs 2.4429

Built-in-potential (V) φbi 0.9

Finger inductance (pH) Lp 50

Parasitic capacitance (fF) Cp 1

Pad-to-pad capacitance (fF) Cpp 15

Bonding inductance (pH) L1 60.13

Bonding inductance (pH) L2 51.36

Pad capacitance (fF) C1 60.34

Pad capacitance (fF) C2 46.26

Bonding resistance (Ω) R 0–3

4. CONCLUSION

In this work, we have described a procedure for characterizingplanar Schottky diodes, based on Direct Current (DC) measurement,capacitance measurements and S parameter measurements, whoseresults are used to find the equivalent large-signal model of Schottky


diodes. These diodes have one of the best price-performance ratios onthe market and we feel that they will become an integral part of manyapplications.

The capability of our characterization and modeling methodhas been demonstrated to create a reliable equivalent circuit modelof Schottky diodes with very good accuracy and valid under largesignal conditions and at high frequencies up to 110GHz. This wasdemonstrated using measurements up to 50 GHz and between 75GHzand 110 GHz, although with a lack of measurements in the 50–75 GHzrange.

Scattering measurements have also been obtained for the assemblyof Coplanar to Microstrip transition-bond wire-Coplanar to Microstriptransition to verify the feasibility of the proposed model used for de-embedding. Simulation and measurements of the assembly indicatesthat the proposed model can describe the behavior of Coplanar toMicrostrip transitions well and it can be used to separate the trueperformance of the diodes from the effect of the elements used in ourtest fixture.

The model was tested under various bias points and results werecompared to the measured data. In all cases, the simulation results areshown to be in good agreement with the measured data. Finally, themodel can be easily implemented in any circuit simulator and appliedto other types of diodes.

ACKNOWLEDGMENT

The authors would like to thank the Spanish Ministries of Scienceand Innovation (MICINN) and of Economy and Competitiveness(MINECO) for the financial support provided through projectsCSD2008-00068, TEC2011-29264-C03-01 and FEDER co-fundedTEC2011-29126-C03-01. The authors express their gratitude to theSpanish Agency AECI though its program ‘Becas para ExtranjerosNo Iberoamericanos para Estudios de Postgrado, Doctorado yPostdoctorado en Universidades y Centros Superiores en Espana’. Theauthors also would like to thank Sandra Pana, Ana Perez and EvaCuerno for their help with the assembly of the devices and DermotErskine for the correction of the text.

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